Question

224 unit 3 practice test

1. given that \\( \triangle a b c \cong \triangle d e f \\), list all of the pairs of congruent sides and angles.

sides:
angles:

Explanation:

Step1: Recall the property of congruent triangles

When \(\triangle ABC\cong\triangle DEF\), the corresponding parts (sides and angles) are congruent. The order of the letters in the congruence statement gives the correspondence. That is, \(A\) corresponds to \(D\), \(B\) corresponds to \(E\), and \(C\) corresponds to \(F\).

Step2: List the congruent sides

For sides:

• \(AB\) corresponds to \(DE\), so \(AB = DE\)
• \(BC\) corresponds to \(EF\), so \(BC=EF\)
• \(AC\) corresponds to \(DF\), so \(AC = DF\)

Step3: List the congruent angles

For angles:

• \(\angle A\) corresponds to \(\angle D\), so \(\angle A=\angle D\)
• \(\angle B\) corresponds to \(\angle E\), so \(\angle B=\angle E\)
• \(\angle C\) corresponds to \(\angle F\), so \(\angle C=\angle F\)

Answer:

Sides: \(AB = DE\), \(BC = EF\), \(AC=DF\)
Angles: \(\angle A=\angle D\), \(\angle B=\angle E\), \(\angle C=\angle F\)